The geodesic diameter of polygonal domains

Sang Won Bae, Matias Korman, Yoshio Okamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this paper, we present the first algorithm that computes the geodesic diameter of a given polygonal domain in worst-case time O(n 7.73) or O(n 7 (logn + h)). Among other results, we show the following geometric observation: the geodesic diameter can be determined by two points in its interior. In such a case, there are at least five shortest paths between the points.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2010 - 18th Annual European Symposium, Proceedings
Pages500-511
Number of pages12
EditionPART 1
DOIs
Publication statusPublished - 2010
Event18th Annual European Symposium on Algorithms, ESA 2010 - Liverpool, United Kingdom
Duration: 2010 Sep 62010 Sep 8

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6346 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other18th Annual European Symposium on Algorithms, ESA 2010
CountryUnited Kingdom
CityLiverpool
Period10/9/610/9/8

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Bae, S. W., Korman, M., & Okamoto, Y. (2010). The geodesic diameter of polygonal domains. In Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings (PART 1 ed., pp. 500-511). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6346 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-15775-2_43